They would be strategically obligued to deny everything, so the answer would "No, no such a thing like UFOs here".
i.e. what happened with the NSA programs, most were almost fully known for the "conspiracy wackos" except by the name of the program, even decades before Snowden. But just were confirmed to be real maybe 30 years after the first mentions in the 70s,80s,90s.
- the alien tech isn't really and/or fully available, they are half way in the reverse engineering efforts, and maybe other powers are in the race too
- the alien tech intrinsically reveals some currently hidden aspect of the universe/reality, if you present the technology publicly, it will be obvious that there's something new, and everybody will pursuit advances related to these new physics.
i.e. imagine discovering the eletricity in the XV century, it would have changed everything.
The question is how you react when the answer is "No." If you keep insisting the government is lying, then you're more and more getting into 'tin foil hat' territory, especially if you're a government employee and have no evidence other than alleged hearsay. It depends on your strength of belief in the contrarian opinion. Saying that it's possible is one thing, saying "they're doing it but I don't have proof" is another.